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A new concentration inequality for the excess risk in least-squares regression with random design and heteroscedastic noise

02/16/2017

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by Adrien Saumard, et al.

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We prove a new concentration inequality for the excess risk of a M-estimator in least-squares regression with random design and heteroscedastic noise. This kind of result is a central tool in modern model selection theory, as well as in recent achievements concerning the behavior of regularized estimators such as LASSO, group LASSO and SLOPE.

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